TY - GEN

T1 - Partitioning a multi-weighted graph to connected subgraphs of almost uniform size

AU - Ito, Takehiro

AU - Goto, Kazuya

AU - Zhou, Xiao

AU - Nishizeki, Takao

PY - 2006

Y1 - 2006

N2 - Assume that each vertex of a graph G is assigned a constant number q of nonnegative integer weights, and that q pairs of nonnegative integers l i and ui, 1 ≤ i ≤ q, are given. One wishes to partition G into connected components by deleting edges from G so that the total i-th weights of all vertices in each component is at least li and at most ui for each index i, 1 ≤ i ≤ q. The problem of finding such a "uniform" partition is NP-hard for series-parallel graphs, and is strongly NP-hard for general graphs even for q = 1. In this paper we show that the problem and many variants can be solved in pseudo-polynomial time for series-parallel graphs. Our algorithms for series-parallel graphs can be extended for partial k-trees, that is, graphs with bounded tree-width.

AB - Assume that each vertex of a graph G is assigned a constant number q of nonnegative integer weights, and that q pairs of nonnegative integers l i and ui, 1 ≤ i ≤ q, are given. One wishes to partition G into connected components by deleting edges from G so that the total i-th weights of all vertices in each component is at least li and at most ui for each index i, 1 ≤ i ≤ q. The problem of finding such a "uniform" partition is NP-hard for series-parallel graphs, and is strongly NP-hard for general graphs even for q = 1. In this paper we show that the problem and many variants can be solved in pseudo-polynomial time for series-parallel graphs. Our algorithms for series-parallel graphs can be extended for partial k-trees, that is, graphs with bounded tree-width.

UR - http://www.scopus.com/inward/record.url?scp=33749573476&partnerID=8YFLogxK

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U2 - 10.1007/11809678_9

DO - 10.1007/11809678_9

M3 - Conference contribution

AN - SCOPUS:33749573476

SN - 3540369252

SN - 9783540369257

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 63

EP - 72

BT - Computing and Combinatorics - 12th Annual International Conference, COCOON 2006, Proceedings

PB - Springer Verlag

T2 - 12th Annual International Conference on Computing and Combinatorics, COCOON 2006

Y2 - 15 August 2006 through 18 August 2006

ER -